This substantial introductory chapter outlines how the camera obscura and the magic lantern contributed to the important intellectual developments at the turn of the seventeenth century. Submitting to the principles of transformation and variation, these media of projection gave expression to a dynamic worldview emerging during the period, especially in Girard Desargues's projective geometry and G. W. Leibniz's philosophy, which challenged established distinctions between change and order, contingency and organization, randomness and design. The chapter furthermore makes an analytical distinction between optical projection and the two other key forms of projection of early modernity: cartographic and perspective projection. Whereas cartographic pictures rendered the earth's surface as a navigable grid, and perspective pictures responded to the needs of perceptually accurate representation, optical projections, the chapter argues, rather overshadowed the real with a transcending frame of reference—which in turn allowed the questioning of the nature of this frame itself.

This chapter focuses on the theological-governmental meanings of projection advanced and articulated by Jesuit scholars during the latter half of the seventeenth century. The Jesuit scholars—Athanasius Kircher at the forefront—modeled the universe based on the principles of projection and reflection of light through mirrors and lenses. The chapter focuses on the metaphysical and epistemic role played by optical media—and the camera obscura, in particular—within Kircher's system. Kircher approached projected images as parallel in their ontological status with nature's miraculous images and conceptualized them as mediators of divine providence on earth. The chapter further explores how the concept of projection qua divine government informed the Catholic Church's colonial project, and the Jesuit order's program of propagating faith through science, focusing on Mexico (in addition to briefly concluding with China) where the most experimental and idiosyncratic takes on optical projection emerged during the period.

This chapter continues the theme of (divine) government introduced in the Chapter 2, developing the notion of "government of souls" (from Michel Foucault). Mapping the early uses of cameras obscuras and magic lanterns as artifices of trick and illusion, the chapter focuses on how Athanasius Kircher and his colleagues developed optical media into techniques of "parastatic magic," in other words, the creation of phantasmatic virtual realities with the pedagogical aim of guiding individuals toward perfection. The chapter highlights Kircher's and his contemporaries' work on the magic lantern and shows how the Jesuits compared the apparatus with the order's spiritual exercises. In this context, the imagination, as the capacity of conjuring and recognizing appearances never perceived by the senses, developed into a critical object of government by technologically mediated means.

In England at the turn of the seventeenth century, the history of optical media intersected with two key "revolutions" of modernity: scientific and financial. This chapter discusses the technologies and concepts of optical projection that emerged within the Royal Society of London. The Royal Society fellows, who pursued the radical reassessment of vision by Johannes Kepler and the new principles of scientific study proclaimed by Francis Bacon, turned devices of projection toward empirical reality. The chapter focuses on Robert Hooke's invention of a portable camera obscura, which illustrates how devices of projection participated in key epistemic developments, in addition to becoming involved in the colonial expansion of both knowledge and trade. Crucial here was the implicit association that Hooke and his contemporaries made between the concepts of projection and property—the latter starting to become relinquished from celestial possession in the writings of John Locke, among others.

This chapter explores how the early media of projection helped making sense of the rapidly developing financial economy in the beginning of the eighteenth century. With the rise of finance, property and value lost their traditional supports and became immaterial, fluctuating, and subject to sudden change. While techniques of "projective" calculation were employed to manage the turbulent movements of finance, the magic lantern's ephemeral images, due to their lack of solidity and stability, provided appropriate mental analogues to make sense of the speculative economy, which had emerged as an ambiguous and illusory perceptual realm seemingly unmoored from material restraints. Overall, the chapter shows how optical media offered cognitive tools to tackle the subsumption of material relations under abstract and invisible, noetic and even imaginary, designs—thus facilitating the development of a new economic concept of the world as an object of speculation.

The epilogue suggests how the historical processes discussed in the book—the Jesuits' global mission of converting souls, the development of the British empire's networks of knowledge and trade, as well as the rise of financial capitalism—each involved an optics of projection as an important visual and cognitive frame that facilitated the abstraction of things and processes within a system of government and profitability. The epilogue also discusses the development of finance after the historical period studied in the book, focusing on how Karl Marx's critique of speculative economy drew on key optical metaphors from the eighteenth century.